Abstract
In this presentation we discuss methods for inverse or parameter estimation problems which can be employed as quantitative modeling techniques in models for distributed (spatially, age, size, etc.) biological systems. In this context they may be useful in attempts to understand, elaborate on, or further refine details of specific mechanisms for dispersal, growth, interaction, etc. in wide classes of models. We have also used these techniques in a number of biologically related problems [1] such as bioturbation [12], [14], [15] and climatology [19]. In addition to an overview of ideas underlying these techniques, we shall present here brief discussions and some findings on two specific biological problems for which we are currently using them successfully.
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References
H.T. Banks, On a variational approach to some parameter estimation problems, Proc. Int. Conf. on Control Theory for Distributed Parameter Systems and Applications (Vorau, Austria, July 9–14, 1984); LCDS Report #85–14, Brown University, May 1985.
H.T. Banks, J.M. Crowley and K. Kunisch, Cubic spline approximation techniques for parameter estimation in distributed systems, IEEE Trans. Auto. Control, AC-28. (1983), 773–786.
H.T. Banks and P. Kareiva, Parameter estimation techniques for transport equations with applications to population dispersal and tissue bulk flow models, J. Math. Biology, 17, (1983), 253–273.
H.T. Banks, P. Kareiva and P.K. Lamm, Estimation techniques for transport equations, Mathematics in Biology and Medicine, Proceedings, Bari 1983, (V. Capasso et al. Eds.), Springer Lecture Notes in Biomath., 57, (1985), 428–438.
H.T. Banks, P.M Kareiva and P.K. Lamm, Modeling insect dispersal and estimating parameters when mark-release techniques may cause initial disturbances, J. Math. Biol., 22, (1985), 259–277.
H.T. Banks, P. Kareiva and L. Zia, Analyzing field studies of insect dispersal with two-dimensional transport equations, to appear.
H.T. Banks and K. Kunisch, An approximation theory for nonlinear partial differential equations with applications to identification and control, SIAM J. Control and Opt. 20, (1982), 815–849.
H.T. Banks and P. Daniel Lamm, Estimation of variable coefficients in parabolic distributed systems, LCDS Report #82–22, Brown University, Sept. 1982;
H.T. Banks and P. Daniel Lamm, Estimation of variable coefficients in parabolic distributed systems, IEEE Trans. Auto. Control, 30, (1985), 386–398.
H.T. Banks and K.A. Murphy, Estimation of coefficients and boundary parameters in hyperbolic systems, LCDS Report #84–5, Brown University, February, 1984;
H.T. Banks and K.A. Murphy, Estimation of coefficients and boundary parameters in hyperbolic systems, SIAM J. Control and Opt, to appear.
H.T. Banks and K.A. Murphy, Estimation of parameters in nonlinear distributed systems, Proc. 23rd IEEE Conference on Decision and Control, Las Vegas, (Dec. 12–14, 1984), 257–261.
H.T. Banks and K.A. Murphy, Estimation of nonlinearities in parabolic models for growth, predation and dispersal of populations, to appear.
H.T. Banks and I.G. Rosen, Fully discrete approximation methods for the estimation of parabolic systems and boundary parameters, LCDS Report #84–19, Brown University, May 1984; Acta. Applic. Math., to appear.
H.T. Banks and I.G. Rosen, A Galerkin method for the estimation of parameters in hybrid systems governing the vibration of flexible beams with tip bodies, CSDL Report R-1724, June 1984; C.S. Draper Labs, Cambridge, MA.
H.T. Banks and I.G. Rosen, Approximation methods for the solution of inverse problems in lake and sea sediment core analysis, Proc. 24th Conf. on Dec. and Control, (Dec. 11–13, 1985), Ft. Lauderdale, 732–736.
H.T. Banks and I.G. Rosen, Numerical schemes for the estimation of functional parameters in distributed models for mixing mechanisms in lake and sea sediment cores, LCDS Report 85–27, Brown University, October 1985.
H.T. Banks and D. Iles, A comparison of stability and convergence properties of techniques for inverse problems, LCDS Report #86–3, Brown University, January 1986.
L. Botsford, B. Vandracek, T. Wainwright, A. Linden, R. Kope, D. Reed, and J.J. Cech, Jr., Population development of the mosquitofish, Gambusia Affinis. in rice fields, preprint.
F. Colonius and K. Kunisch, Stability for parameter estimation in two point boundary value problems, Inst. fur Math. Bericht No. 50–1984, Tech. Univ. Graz, October, 1984.
F. Dexter, H.T. Banks and T. Webb, Modeling Holocene changes in the location and abundance of beach populations in eastern North America, J. Biogeography, to be submitted.
D. Gottlieb and S. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1977.
Kareiva, P., Experimental and mathematical analysis of movement: quantifying the influence of plant spacing and quality on foraging discrimination, Ecol. Mon. 52 (1982) 261–282.
Kareiva, P., Local movement in herbivorous insects: applying a passive diffusion model to mark-recapture field experiments, Oecologia (Berl.) 57, (1983) 322–327.
Kareiva, P., Influence of vegetation texture on herbivore populations: resource concentration as herbivore movement. In Denno & McClure (eds.) Variable Plants and Herbivores in Natural and Managed Systems. New York: Academic Press (1983).
Kareiva, P., Predator-prey dynamics in spatially-structured populations: manipulating dispersal in a coccinellid-aphid interaction. Springer Lect. Notes in Biomathematics, 54. (1984) 368–389.
K. Kunisch and L.W. White, Identifiability under approximation for an elliptic boundary value problem, SIAM J. Control and Opt., to appear.
A. Okubo, Diffusion and Ecological Problems: Mathematical Models, Springer-Verlag, New York, 1980.
MH. Schultz, Spline Analysis, Prentice Hall, Englewood Cliffs, 1973.
N. Shigesada, K. Kawasaki and E. Teramoto, Spatial segregation of interacting species, J. Theor. Biol. 79, (1979), 83–99.
N. Shigesada and E. Teramoto, A consideration on the theory of environmental density, Japanese J. Ecol., 28 (1978), 1–8.
T.C. Wainwright, R.G. Kope, L.W. Botsford, and J.J. Cech Jr., Implications of laboratory mosquitofish experiments for population development in rice fields, Proc. 52nd Conf. Calif. Mosquito and Vector Control Assoc. (Jan. 29–Feb. 1, 1984).
L.L. Zia, Parameter Estimation Techniques for Two-dimensional Transport Equations with Application to Models of Insect Dispersal, Ph.D. Thesis, Brown University, May 1985.
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Banks, H.T., Murphy, K.A. (1987). Quantitative Modeling of Growth and Dispersal in Population Models. In: Teramoto, E., Yumaguti, M. (eds) Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Lecture Notes in Biomathematics, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93360-8_10
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DOI: https://doi.org/10.1007/978-3-642-93360-8_10
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